Fusion of natural language propositions: Bayesian random set framework

This work concerns an automatic information fusion scheme for state estimation where the inputs (or measurements) that are used to reduce the uncertainty in the state of a subject are in the form of natural language propositions. In particular, we consider spatially referring expressions concerning the spatial location (or state value) of certain subjects of interest with respect to known anchors in a given state space. The probabilistic framework of random-set-based estimation is used as the underlying mathematical formalism for this work. Each statement is used to generate a generalized likelihood function over the state space. A recursive Bayesian filter is outlined that takes, as input, a sequence of generalized likelihood functions generated by multiple statements. The idea is then to recursively build a map, e.g. a posterior density map, over the state space that can be used to infer the subject state.